{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "48922578-ec38-4b57-a767-893667b65139",
   "metadata": {},
   "source": [
    "Chapter 02\n",
    "\n",
    "# 回归分析\n",
    "Book_7《机器学习》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "163cd697-9f72-41b3-8328-1048d8986d05",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import yfinance as yf\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5e8915e6-3f87-4195-bc9b-d847a87a092c",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = plt.rcParams\n",
    "p[\"font.sans-serif\"] = [\"Roboto\"]\n",
    "p[\"font.weight\"] = \"light\"\n",
    "p[\"ytick.minor.visible\"] = False\n",
    "p[\"xtick.minor.visible\"] = False\n",
    "p[\"axes.grid\"] = True\n",
    "p[\"grid.color\"] = \"0.5\"\n",
    "p[\"grid.linewidth\"] = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d251ef26-cdbf-4c42-80c7-d2111e132c08",
   "metadata": {},
   "source": [
    "## 下载、处理数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4455ec98-55c4-4f46-899e-f4b958f3edb6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%%**********************]  2 of 2 completed\n"
     ]
    }
   ],
   "source": [
    "y_x_df = yf.download(['AAPL','^GSPC'], start='2020-01-01', end='2020-12-31')\n",
    "y_x_df = y_x_df['Adj Close'].pct_change()\n",
    "y_x_df.dropna(inplace = True)\n",
    "\n",
    "y_x_df.rename(columns={\"^GSPC\": \"SP500\"},inplace = True)\n",
    "y_x_df.to_pickle('y_x_df.pkl')\n",
    "# 如果不能下载数据，请用pandas.read_pickle() 从配套文件读入数据\n",
    "x_df = y_x_df[['SP500']]\n",
    "y_df = y_x_df[['AAPL']]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9dc25fa-e171-49e6-b091-5be88b7fbe18",
   "metadata": {},
   "source": [
    "## 线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c1f9e7f2-4e3b-4b2c-bff9-d97c57c5ddb4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   AAPL   R-squared:                       0.689\n",
      "Model:                            OLS   Adj. R-squared:                  0.687\n",
      "Method:                 Least Squares   F-statistic:                     550.5\n",
      "Date:                Mon, 01 Jan 2024   Prob (F-statistic):           5.16e-65\n",
      "Time:                        07:28:57   Log-Likelihood:                 675.37\n",
      "No. Observations:                 251   AIC:                            -1347.\n",
      "Df Residuals:                     249   BIC:                            -1340.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0019      0.001      1.819      0.070      -0.000       0.004\n",
      "SP500          1.1233      0.048     23.462      0.000       1.029       1.218\n",
      "==============================================================================\n",
      "Omnibus:                       52.109   Durbin-Watson:                   1.871\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              210.794\n",
      "Skew:                           0.772   Prob(JB):                     1.69e-46\n",
      "Kurtosis:                       7.216   Cond. No.                         46.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# add a column of ones\n",
    "X_df = sm.add_constant(x_df)\n",
    "\n",
    "model = sm.OLS(y_df, X_df)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4b0d158e-8300-42f6-9975-287d08c12c78",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_params = model.fit().params\n",
    "\n",
    "x_mean = x_df.mean().values\n",
    "y_mean = y_df.mean().values\n",
    "\n",
    "n = len(y_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b5cbeee2-df19-45da-b411-848697753595",
   "metadata": {},
   "outputs": [],
   "source": [
    "# predicted\n",
    "y_hat = results.fittedvalues\n",
    "\n",
    "y_hat = y_hat.to_frame()\n",
    "y_hat = y_hat.rename(columns={0: 'AAPL'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ffe98d08-7f67-48f3-8fc4-1441869e4f50",
   "metadata": {},
   "outputs": [],
   "source": [
    "DFR = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dfe0bb0b-3e4a-45c5-a655-538585487222",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sum of Squares for Error, SSE\n",
    "SSE = ((y_df - y_hat)**2).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ec99277b-95ab-48c8-9269-f302dc358b90",
   "metadata": {},
   "outputs": [],
   "source": [
    "# degrees of freedom for error, DFE\n",
    "DFE = n - DFR - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2669b0e3-4358-4dd0-9049-6a40d0c368b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean squared error, MSE\n",
    "# MSE = SSE/DFE\n",
    "# MSE = MSE.values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a69afa1-e989-4c9d-81e3-60bc7d488821",
   "metadata": {},
   "source": [
    "## t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5c5ae0c4-1e23-44ff-91a2-be94c34fa9e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[23.46167122]\n"
     ]
    }
   ],
   "source": [
    "MSE = SSE/DFE\n",
    "MSE = MSE.values\n",
    "# 计算MSE\n",
    "\n",
    "b1 = model_params.SP500\n",
    "# 斜率系数\n",
    "\n",
    "SSD_x = np.sum((x_df.values - x_mean)**2)\n",
    "\n",
    "SE_b1 = np.sqrt(MSE/SSD_x)\n",
    "# 标准误\n",
    "\n",
    "T_b1 = (b1 - 0)/SE_b1\n",
    "# b1的t检验统计量\n",
    "print(T_b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0cb90895-2f24-47f3-ab66-70ef71ea061d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.81883761]\n"
     ]
    }
   ],
   "source": [
    "b0 = model_params.const\n",
    "# 截距系数\n",
    "\n",
    "SE_b0 = np.sqrt(MSE*(1/n + x_mean**2/SSD_x))\n",
    "# 标准误\n",
    "\n",
    "T_b0 = (b0 - 0)/SE_b0\n",
    "# b0的t检验统计量\n",
    "\n",
    "print(T_b0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "900991dc-eb05-4a7c-a848-a25015e8c3d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.1637086e-65]\n",
      "[0.0701374]\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "pval_b1 = stats.t.sf(np.abs(T_b1), n-2)*2\n",
    "print(pval_b1)\n",
    "pval_b0 = stats.t.sf(np.abs(T_b0), n-2)*2\n",
    "print(pval_b0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34252af9-40d1-49c7-a838-2bbd49b097b4",
   "metadata": {},
   "source": [
    "## confidence intervals of coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e4a86e5e-2d05-415a-b297-1579b5df2894",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.2176517]\n",
      "[1.02904801]\n",
      "[0.0039431]\n",
      "[-0.00015685]\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "# 显著水平\n",
    "t_95 = stats.t.ppf(1 - alpha/2, DFE) \n",
    "# t值\n",
    "\n",
    "# 系数b1的1 – α 置信区间\n",
    "b1_upper_95 = b1 + t_95*SE_b1\n",
    "print(b1_upper_95)\n",
    "b1_lower_95 = b1 - t_95*SE_b1\n",
    "print(b1_lower_95)\n",
    "\n",
    "# 系数b0的1 – α 置信区间\n",
    "b0_upper_95 = b0 + t_95*SE_b0\n",
    "print(b0_upper_95)\n",
    "b0_lower_95 = b0 - t_95*SE_b0\n",
    "print(b0_lower_95)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae97562d-bf1b-428c-8f66-1ad760f1df1e",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "238d3510-ca8b-4da3-80b7-9140ed66d005",
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate x-values for regression line\n",
    "x_i = np.linspace(-0.15,0.15,50)\n",
    "\n",
    "# predicted values\n",
    "y_i = b0 + b1* x_i\n",
    "\n",
    "alpha = 0.05\n",
    "t_95 = stats.t.ppf(1 - alpha/2, DFE) \n",
    "\n",
    "CI_95 = t_95 * np.sqrt(MSE) * np.sqrt(1/n + (x_i - x_mean)**2 / np.sum((x_df.values - x_mean)**2))\n",
    "\n",
    "CI_upper_95 = y_i + CI_95\n",
    "CI_lower_95 = y_i - CI_95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6a78f68f-f293-4aaa-83ba-2251803bf487",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "t_99 = stats.t.ppf(1 - alpha/2, DFE) \n",
    "\n",
    "CI_99 = t_99 * np.sqrt(MSE) * np.sqrt(1/n + (x_i - x_mean)**2 / np.sum((x_df.values - x_mean)**2))\n",
    "\n",
    "CI_upper_99 = y_i + CI_99\n",
    "CI_lower_99 = y_i - CI_99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0707ed47-8821-48f4-997f-bedbb770bbd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.15, 0.15)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# confidence band\n",
    "fig, ax = plt.subplots()\n",
    "plt.scatter(x_df, y_df, alpha = 0.5)\n",
    "\n",
    "plt.plot(x_i, y_i,color = 'r')\n",
    "\n",
    "# plot confidence interval\n",
    "ax.fill_between(x_i,CI_lower_95, CI_upper_95, color = 'b', alpha = 0.5)\n",
    "ax.fill_between(x_i,CI_lower_99, CI_upper_99, color = 'b', alpha = 0.25)\n",
    "\n",
    "plt.axis('scaled')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.xlim([-0.15,0.15])\n",
    "plt.ylim([-0.15,0.15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a3008cd0-be8e-437f-b4be-00cac26324c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>SP500</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-01-03</th>\n",
       "      <td>-0.009722</td>\n",
       "      <td>-0.007060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-06</th>\n",
       "      <td>0.007968</td>\n",
       "      <td>0.003533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-07</th>\n",
       "      <td>-0.004703</td>\n",
       "      <td>-0.002803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-08</th>\n",
       "      <td>0.016086</td>\n",
       "      <td>0.004902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-09</th>\n",
       "      <td>0.021241</td>\n",
       "      <td>0.006655</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL     SP500\n",
       "Date                          \n",
       "2020-01-03 -0.009722 -0.007060\n",
       "2020-01-06  0.007968  0.003533\n",
       "2020-01-07 -0.004703 -0.002803\n",
       "2020-01-08  0.016086  0.004902\n",
       "2020-01-09  0.021241  0.006655"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_x_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "69c0bb27-2769-4836-967a-74c42705580c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.13052396701224492,\n",
       " 0.10451115437058604,\n",
       " -0.15820923621203722,\n",
       " 0.13304707646682348)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# linear regression with confidence interval, Seaborn\n",
    "\n",
    "sns.regplot(y_x_df, x = 'SP500', y = 'AAPL', ci=95)\n",
    "plt.axis('scaled')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "04a8bd38-2d31-402a-bf60-6bcb2b7d2093",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.13052396701224492,\n",
       " 0.10451115437058604,\n",
       " -0.16235468050658938,\n",
       " 0.1348652649958163)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(y_x_df, x = 'SP500', y = 'AAPL', ci=99)\n",
    "plt.axis('scaled')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ccf38b1b-d0a3-44cc-b63d-2aeaec265910",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05\n",
    "t_95 = stats.t.ppf(1 - alpha/2, DFE) \n",
    "\n",
    "pi_95 = t_95 * np.sqrt(MSE) * np.sqrt(1 + 1/n + (x_i - x_mean)**2 / np.sum((x_df.values - x_mean)**2))\n",
    "\n",
    "pi_upper_95 = y_i + pi_95\n",
    "pi_lower_95 = y_i - pi_95\n",
    "\n",
    "alpha = 0.01\n",
    "t_99 = stats.t.ppf(1 - alpha/2, DFE) \n",
    "\n",
    "pi_99 = t_99 * np.sqrt(MSE) * np.sqrt(1 + 1/n + (x_i - x_mean)**2 / np.sum((x_df.values - x_mean)**2))\n",
    "\n",
    "pi_upper_99 = y_i + pi_99\n",
    "pi_lower_99 = y_i - pi_99"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c228336-9b52-4856-afd2-f303cae64f06",
   "metadata": {},
   "source": [
    "## plot predicting interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9d51bae4-5734-4f47-bee3-992418963834",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.15, 0.15)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plt.scatter(x_df,y_df, zorder = 10, \n",
    "            color = 'b', alpha = 0.25); \n",
    "\n",
    "plt.plot(x_i, y_i,color = 'r')\n",
    "\n",
    "\n",
    "ax.fill_between(x_i,pi_lower_95, pi_upper_95, color = 'b', alpha = 0.25)\n",
    "ax.fill_between(x_i,pi_lower_99, pi_upper_99, color = 'b', alpha = 0.25)\n",
    "\n",
    "plt.axis('scaled')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.xlim([-0.15,0.15])\n",
    "plt.ylim([-0.15,0.15])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "accb3c77-0ed9-47e2-b1e8-6d3f148d9a7c",
   "metadata": {},
   "source": [
    "## Log-Likelihood Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e5587b5e-2742-4ade-9e64-c1c66595ad68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL    675.366503\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# SSE = SSE.values\n",
    "s2 = SSE / n\n",
    "\n",
    "# maximum likelihood estimator of error variance\n",
    "# Log Likelihood function\n",
    "log_L = n*(-np.log(np.sqrt(s2*2*np.pi))) - n/2\n",
    "print(log_L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ee1d8468-59ad-4add-8202-ecd943b74208",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL   -1346.733006\n",
      "dtype: float64\n",
      "AAPL   -1339.682101\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "AIC = 2*(DFR + 1) - 2*log_L\n",
    "print(AIC)\n",
    "BIC = (DFR + 1)*np.log(n) - 2*log_L\n",
    "print(BIC)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af562c27-115a-4767-b1a8-262f93f7df54",
   "metadata": {},
   "source": [
    "## Residual analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fbc67647-7fe9-4c60-af82-2b842b879bd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "e_df = y_df - y_hat;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "05d8ce29-c85e-466f-99b2-92a47ddd06f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.15, 0.15)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# confidence band\n",
    "fig, ax = plt.subplots()\n",
    "plt.scatter(x_df,e_df, alpha = 0.5); \n",
    "plt.axhline(y=0, color='r', linestyle='--')\n",
    "plt.axis('scaled')\n",
    "plt.ylabel('y')\n",
    "plt.xlabel('x')\n",
    "plt.xlim([-0.15,0.15])\n",
    "plt.ylim([-0.15,0.15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4c5d4fd5-41d1-4310-ac57-28d0f5d5b429",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL    0.7719\n",
      "dtype: float64\n",
      "[0.77189976]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\james\\anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:3472: FutureWarning: In a future version, DataFrame.mean(axis=None) will return a scalar mean over the entire DataFrame. To retain the old behavior, use 'frame.mean(axis=0)' or just 'frame.mean()'\n",
      "  return mean(axis=axis, dtype=dtype, out=out, **kwargs)\n",
      "C:\\Users\\james\\anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:3472: FutureWarning: In a future version, DataFrame.mean(axis=None) will return a scalar mean over the entire DataFrame. To retain the old behavior, use 'frame.mean(axis=0)' or just 'frame.mean()'\n",
      "  return mean(axis=axis, dtype=dtype, out=out, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "# skewness\n",
    "S = np.mean(e_df**3)/np.mean(e_df**2)**(3/2)\n",
    "print(S)\n",
    "S_2 = stats.skew(e_df,bias = True)\n",
    "print(S_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18e693e1-5d3b-4ae6-a638-5317e0a2ff33",
   "metadata": {},
   "source": [
    "## kurtosis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "96a3e1bd-9c5f-4f4f-9000-807ca571e1b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL    7.215717\n",
      "dtype: float64\n",
      "[7.21571709]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\james\\anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:3472: FutureWarning: In a future version, DataFrame.mean(axis=None) will return a scalar mean over the entire DataFrame. To retain the old behavior, use 'frame.mean(axis=0)' or just 'frame.mean()'\n",
      "  return mean(axis=axis, dtype=dtype, out=out, **kwargs)\n",
      "C:\\Users\\james\\anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:3472: FutureWarning: In a future version, DataFrame.mean(axis=None) will return a scalar mean over the entire DataFrame. To retain the old behavior, use 'frame.mean(axis=0)' or just 'frame.mean()'\n",
      "  return mean(axis=axis, dtype=dtype, out=out, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "K = np.mean(e_df**4)/np.mean(e_df**2)**(4/2)\n",
    "print(K)\n",
    "K_2 = stats.kurtosis(e_df,fisher=False,bias = True)\n",
    "print(K_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a7b8d6e-a8ad-4327-b16c-277f5dce2b6c",
   "metadata": {},
   "source": [
    "## Omnibus test for normality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "363e2d66-06f8-4b5f-bd83-dd822bc6961a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[52.10899919]\n"
     ]
    }
   ],
   "source": [
    "(Omnibus_test, p) = stats.normaltest(e_df)\n",
    "print(Omnibus_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d9936766-d575-446c-8cee-ee35e1f7f337",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\james\\AppData\\Local\\Temp\\ipykernel_15768\\2583923896.py:2: UserWarning: \n",
      "\n",
      "`distplot` is a deprecated function and will be removed in seaborn v0.14.0.\n",
      "\n",
      "Please adapt your code to use either `displot` (a figure-level function with\n",
      "similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "\n",
      "For a guide to updating your code to use the new functions, please see\n",
      "https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751\n",
      "\n",
      "  sns.distplot(e_df)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "sns.distplot(e_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8854a31f-e03b-45ee-b84a-1462772d929f",
   "metadata": {},
   "source": [
    "## Jarque-Bera test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2c5be62f-ac7f-4069-9917-0fcc933eac82",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL    210.793853\n",
      "dtype: float64\n",
      "[0.]\n"
     ]
    }
   ],
   "source": [
    "JB = (n/6.0) * ( S**2.0 + (1.0/4.0)*( K - 3.0 )**2.0 )\n",
    "print(JB)\n",
    "p_JB = 1.0 - stats.chi2(2).cdf(JB)\n",
    "print(p_JB)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90c1876d-f7e7-4e33-b9d8-afadabd46caa",
   "metadata": {},
   "source": [
    "## Autocorrelation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "dfd03ebd-90e3-4618-83ed-e6da80b3d090",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot\n",
    "from statsmodels.graphics.tsaplots import plot_acf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb2e7684-1a5f-4a15-8353-1132f378294a",
   "metadata": {},
   "source": [
    "## Durbin-Watson test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "4d302426-8946-4a0c-8d84-5f84b20b9abd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAPL    1.871483\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "DW = np.sum(np.diff(e_df['AAPL'].values)**2)/SSE\n",
    "print(DW)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8f034eeb-042d-41b9-babb-75b4c0a2bd26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(e_df, lags=20)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63dd6047-b9fe-4277-9609-8df66bed71ee",
   "metadata": {},
   "source": [
    "## Condition number, multicollinearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "bd31d552-f6fb-4f7e-9d36-dc6dfaeefbef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.51000153e+02 1.18460204e-01]\n",
      "46.03103654981152\n"
     ]
    }
   ],
   "source": [
    "X = np.matrix(X_df)\n",
    "eigen_values, V = np.linalg.eig(X.T * X)\n",
    "print(eigen_values)\n",
    "\n",
    "condition_number = np.sqrt(eigen_values.max()/eigen_values.min())\n",
    "print(condition_number)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
